When you watch or listen to good group improvisers with an eye or ear aimed toward discerning rules and order out of what is apparently chaos and pure spontaneity, one the first things that leaps out at you is the readily repeated pattern of "yes...and-ing". That is, when a group member first introduces a new name, object, objective, phrase or whatever into the shared collective "frame" of the group, the implicit rule obeyed by successful improvisers is to always take in or accept the new element being introduced, as well as the changes to the collective frame it brings with it, and then immediately add to or begin to build off of this new change. This is what "yes...and-ing" means: good improvisers always take what they are given by their group mates, and spin it into gold, so to speak. The only rule is that you cannot refuse a cue or a direction or a decision made by a partner.
The "...and-ing" is just as important as the "yes-ing". Taking the groundwork that others have laid and doing with it what you will, making it your own in the process is a way of acknowledging or recognizing your improv partners and their contributions to what is essentially a collaborative activity. This is why refusing to follow this convention makes for both bad improvisation and often leaves your partners to improv feeling disrespected. More on this below.
But "and-ing" is just as important, for it is a way of "showing off your chops" as a player of the game. Anyone who understands the rules of improv can take part in the game, but it takes real talent to be able to add something interesting, intriguing, or poignant since the material you have to work with is partially contributed by others. Above all, through creative "...and-ing," talented and the well-prepared performers distinguish themselves by making their contributions count, creating interesting hooks and setups for the next performer.
It is not surprising, then, that when asked to describe their craft and the kinds of skills they use to perform it well, improvisers themselves often resort to metaphors and images of balance and self-composition; of being in a "groove" with their partners that allows them to take risks and venture successful anticipations. And, above all, the metaphors improvisers use to describe their craft is of finding a way to maintain the right kind of poise.
This is why group improvisation is often described (by folks like Henry Louis Gates and Ralph Ellison) as all about drawing out bits and pieces of who you are, thus taking significant risks, and making gold out of the hay you've been handed. "...and-ing" is how the best performers show what they can do and (at the same time) a little bit of who they are. Being denied the chance to yourself deny how another person changes the terms of the game at any given time is a lot like gradually spinning out of control on a slick, icy surface. You can struggle against the pull of the spin, but experience tells us that that just makes things worse. Rather, one of the chief skills of the improviser is the ability to maintain the appropriate balance on the icy surface. This requires quick thinking, good anticipation, and a "feel" for when to turn into the slide and when to turn away. And, above all, a knack for remaining always in control. It's no surprise that world-class improvisers are some of the most attentive and sharp-witted individuals, a la Stephen Colbert (a self-identified d&d player, BTW).
Now d&d is obviously more than just group improvisation. This is even true of the older, more "free form" editions. But it is partially about improvisation. DM's clearly are not equals with players when it comes to the ability to add to or change their "shared" fantasy world, that is true. The DM, of course, remains entirely responsible for almost all of the explicit world-building and for running every aspect of the game outside of the PCs themselves. But there are few DM's who run such a tight ship as is technically within their rights. Existing along a spectrum, most good DM's allow a good to the contribution of the player, from ideas about histories to cultures and economies, and so much more. While they are not equals, good DMs and players practice "yes...and-ing" all the time, with the result being the "thickly" described, shared world that we've all experienced when the game's played at its best.
Above all, you notice the rule "yes...and-ing" when it isn't being followed. You find beginning improvisers are most prone to mistakes in this regard. What the rule aims to prevent is the denial of some contribution of a fellow group member just doesn't fit with the direction that another player has decided the improvisation is to take. This is precisely the admittedly exaggerated weakness of rookie improvisers such as "The Office"'s Michael Scott, who is repeatedly banned from his group improv class, because he cannot seem to NOT dominate what is supposed to be a truly collaborative exercise. Michael Scott was famous for twisting and turning (and sometimes telling others that their contributions to the improv were just plain wrong) in order to make every improvised scene into a gun battle in which he alone always emerges victorious.
Such behavior brings attempts at group improvisation to a screeching halt. But, more than that, it is also experienced as a kind of disrespect by fellow improvisers, and not simply as just a failure in performance. This is because, as mentioned above, the act of improvisation itself seduces you into opening yourself up to others in a potentially risky way. And so every "No" you receive is magnified in a very real sense.
Unfortunately the kind of failures in "yes...and-ing" that experienced players and DM's encounter are rarely as obvious as this. But even when they are more subtle, they are are often still just failures to abide this relatively straightforward rule. For example, Boris, a PC dwarven fighter who, at a crucial moment in an encounter "reveals" that he is actually the long, lost nephew of the crypt keeper and that he, therefore, "knows best" how to negotiate with his kin is doing more than grinding the collaborative action to a halt; he is tacitly insulting his companions by challenging the DM to explicitly stop the flow of the game and break Rule 1.
DM's, too, can make mistakes related to the rule of "yes...and-ing" besides the obvious. For example, when a DM allows players the freedom to explore and fully develop backstories for ancillary parts of their PC - such as a familiar - it is of the utmost importance that the DM respect that story and its details. Any failures on the DM's part to remember important details contributed by the player are likely to be experienced as doubly injurious on the part of the player precisely because it is experienced as a kind of disrespect - a violation of the implicit agreement to abide by Rule 1.
Even a well-meaning DM can run afoul of this if she tries to incorporate elements of the a PC backstory into the events of the campaign (not necessarily a bad idea by itself), yet resorts to tactics that effectively strong arm the PC into a particular course of action as a result (e.g., A mysterious letter arrives from someone who is - and not just claims to be - a long-lost son). Or, the DM who attempts to build off the contributed backstory of a familiar, but who completely mischaracterizes, say, the basic nature of the relationship as originally described by the player.
These are simple and relatively easy errors and certainly forgivable. But they're instructive for what they confirm about the importance of "yes...and-ing" to successful improvisational performances. Good DM's and players intuitively know this and try to keep sharp and observant and look for creative ways to keep the game going and "setup" up their partners.